Question: A local gift shop sold bags of candy and cookies for Halloween. Bags of candy cost $$8.00$, and bags of cookies cost $$2.50$, and sales equaled $$52.00$ in total. There were $4$ more bags of cookies than candy sold. Find the number of bags of candy and cookies sold by the gift shop.
Let $x$ equal the number of bags of candy and $y$ equal the number of bags of cookies. The system of equations is then: ${8x+2.5y = 52}$ ${y = x+4}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${x+4}$ for $y$ in the first equation. ${8x + 2.5}{(x+4)}{= 52}$ Simplify and solve for $x$ $ 8x+2.5x + 10 = 52 $ $ 10.5x+10 = 52 $ $ 10.5x = 42 $ $ x = \dfrac{42}{10.5} $ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $ {y = x+4}$ to find $y$ ${y = }{(4)}{ + 4}$ ${y = 8}$ You can also plug ${x = 4}$ into $ {8x+2.5y = 52}$ and get the same answer for $y$ ${8}{(4)}{ + 2.5y = 52}$ ${y = 8}$ $4$ bags of candy and $8$ bags of cookies were sold.